---
title: "Magnetic tension and the growth of a disk disturbance"
description: "Follow MRI from angular-momentum transfer and local equations to mesh convergence, saved-field checks and a paper guide beyond linear growth."
canonical_url: "https://sandboxphysics.com/stories/magnetorotational-instability/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/magnetorotational-instability/"
last_modified: "2026-11-13"
---

Astronomy reading

# Magnetic tension and the growth of a disk disturbance

Sandbox Physics · 2026-11-12

Start with magnetic tension carrying angular momentum outward. Derive the local channel equations, test mesh and time errors, then inspect the saved fields. The final guide follows a published nonideal simulation study beyond the linear model.

1. L1 · Concept

   ## [Who carries angular momentum through an accretion disk?](https://sandboxphysics.com/stories/magnetorotational-instability/who-carries-angular-momentum/)

   Magnetic tension can carry angular momentum outward and draw energy from differential rotation. Follow the feedback in a small growing channel.

2. L2 · Derivation and worked examples

   ## [Four real fields in a rotating patch of a disk](https://sandboxphysics.com/stories/magnetorotational-instability/four-fields-in-a-rotating-patch/)

   Define coordinates and magnetic velocity units, then derive the four real linear equations from one sine and cosine field pattern.

3. L2 · Derivation and worked examples

   ## [Predict the growth, then follow its energy](https://sandboxphysics.com/stories/magnetorotational-instability/growth-stress-and-energy/)

   Derive the channel growth rate, separate velocity and magnetic stresses, and compare energy gain with shear work in one saved field.

4. L2 · Derivation and worked examples

   ## [Why a vertical mesh changes a linear channel](https://sandboxphysics.com/stories/magnetorotational-instability/why-a-vertical-mesh-changes-a-channel/)

   Derive the centered mesh derivative, read actual spatial errors, and distinguish sampled perturbation fields from their four observed amplitudes.

5. L2 · Method guide

   ## [Checking growth, transport and shear work](https://sandboxphysics.com/stories/magnetorotational-instability/checking-growth-and-shear-work/)

   Separate spatial and temporal errors, compare stage-stress work with field energy, and identify what the channel divergence check tests.

6. L3 · Method guide

   ## [Check an MRI calculation from its saved fields](https://sandboxphysics.com/stories/magnetorotational-instability/check-saved-mri-fields/)

   Inspect saved MRI channel fields, recover stress and shear work, and separate spatial from temporal error.

7. L4 · Method guide

   ## [Read beyond linear MRI growth](https://sandboxphysics.com/stories/magnetorotational-instability/read-beyond-linear-mri/)

   Read a Hall and ambipolar MRI figure, then compare net flux and pressure-normalized transport with linear growth.